An apology to Androcles
in [Relativity]
|
From: Androcles on 31 Jul 2010 02:52 "Uncle Ben" <ben(a)greenba.com> wrote in message news:d43195e9-25ef-4d41-a9e9-7abd267e0345(a)c10g2000yqi.googlegroups.com... This subject has been discussed often, and in some discussions Androcles ha progressed all the way to a length comparison, following Einstein's 1905 paper. I now believe he has got it all right except for the final step, which is assigning values to x' and xi. ============================================== As everybody knows, "everybody knows" is Bonehead's preferred method of proof. Let's assign some values. As usual, v = 0.866c so that everybody knows (EVERYBODY!! knows) gamma = Einstein's beta = 1/sqrt(1-v^2) = 1/sqrt(1 - 3/4) = 1/sqrt(1/4) = 1/0.5 = 2. (Everybody knows for v = 0, gamma = 1 and the result is Newtonian) For a rod of length 1 with speed 0, xi = x' = 1/1 = 1. Not everybody knows xi > x' and xi = x' * gamma, so xi = 2, but everybody believes the rod gets shorter. Hence everybody doesn't believe what everybody knows. Everybody knows by accelerating from 0 to 0.866c the rod gradually increases its length from 1 to 2 but everybody believes it gets shorter because everybody can't trust their arithmetic and would prefer to trust their intuition to bleat whatever the rest of the sheep bleat. Some everybodies are stupid sheep in wolf's clothing, but don't fool the wolf. The faster the rod goes the longer it gets and everybody knows its clock slows down to 0.5 seconds per second. So don't go fast, you'll have further to go if you do, which is why the turtle won the race and the hare lost as everybody knows. The absurdity of this error is the point of this thread as everybody knows. ================================================ He agrees in the meaning of the variables x' and xi, including correctly that x' < xi. Where he goes off the track is to insist that x'=L, and therefore xi= Lgamma. The correct path is to assign xi=L and conclude that x' = L/gamma. The absurdity of this error is the point of this thread. Uncle Ben ============================================== Bonehead agrees in the meaning of the variables x' and xi, including correctly that x' < xi. Where he goes off the track is to not insist that x'=L, and therefore xi= Lgamma. The correct path is to assign xi=L*2 and conclude that x' = 1 as everybody knows. The absurdity of this error is the point of this thread, as everybody knows. Atrocious Androcles.
From: ben6993 on 31 Jul 2010 08:36 On Jul 31, 3:49 am, Uncle Ben <b...(a)greenba.com> wrote: > On Jul 30, 9:39 pm, blackhead <larryhar...(a)softhome.net> wrote: > > > > > > > On 31 July, 01:46, Uncle Ben <b...(a)greenba.com> wrote: > > > > On Jul 30, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Jul 30, 3:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > An apology to Androcles > > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > > sci.physics.relativity, was an error of confusing frames of > > > > > reference. But I was wrong. > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > where x' is the length of a moving rod with respect to a stationary > > > > > frame of reference K and xi is the length of the moving rod with > > > > > respect to a frame k comoving with it. My difference with Androcles > > > > > was that I claimed that xi is the proper length L of the rod and the > > > > > shorter x' is a contracted length L/gamma. > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > > insists that x' is L and xi is an expanded length Lgamma. The proper > > > > > length of the rod in k increases because of the existence of another > > > > > frame of reference K moving with respect to it. (This other frame K is > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > considered moving the other way with respect to the rest frame k of > > > > > the rod.) > > > > > > This startling fresh idea would never have occurred to me without > > > > > Androcles's guidance. > > > > > > It seems strange that a nearby frame of reference K, by its relative > > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > > while the rod maintains a constant length with respect to K itself. > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > > on my cigar that had length L when I bought it. It seems strange that > > > > > to you the cigar has length L, but because I am flying within your > > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > > idea that you are down there. > > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > > Uncle Ben > > > > > In this rare instance of someone abandoning their constant delusional > > > > denial state of existence, any chance you can take it a step further > > > > and answer the following? > > > > > Will the ripple eventually reach the Earth? If not then why not? > > > > > 'Hubble Finds Ghostly Ring of Dark Matter'http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_featur... > > > > > "Astronomers using NASAs Hubble Space Telescope got a first-hand view > > > > of how dark matter behaves during a titanic collision between two > > > > galaxy clusters. The wreck created a ripple of dark matter, which is > > > > somewhat similar to a ripple formed in a pond when a rock hits the > > > > water." > > > > > The ripple will eventually reach the Earth and this is evidence dark > > > > matter exists from the galaxy cluster to the Earth. This is evidence > > > > dark matter is the medium of space in which light waves propagate. > > > > > Pressure exerted towards matter by dark matter displaced by the matter > > > > is gravity.- Hide quoted text - > > > > > - Show quoted text - > > > > I have no idea, and this thread is abought the Einstein Expansion.- Hide quoted text - > > > > - Show quoted text - > > > Androcles rechristened the space LT as "Einstein's expansion" formula: > > > xi = x'/sqrt(1 - v^2/c^2) with x' = x-vt > > 1905 paper. > > Used correctly, it transforms x coordinates of the same event between > > different frames, not lengths directly. Androcles plugs in lengths for > > xi, x' without considering what's involved in measuring a length. For > > a start, it involves measuring space coordinates at the *same* time > > and subtracting them from one another to get a length, if it's moving > > in that frame. If the end points remain at the same locations for all > > time, then simultaneity doesn't matter.- Hide quoted text - > > > - Show quoted text - > > Some ng history, Blackhead: > > This subject has been discussed often, and in some discussions > Androcles ha progressed all the way to a length comparison, following > Einstein's 1905 paper. I now believe he has got it all right except > for the final step, which is assigning values to x' and xi. He agrees > in the meaning of the variables x' and xi, including correctly that > x' < xi. Where he goes off the track is to insist that x'=L, and > therefore xi= Lgamma. The correct path is to assign xi=L and conclude > that x' = L/gamma. > > The absurdity of this error is the point of this thread. > > Uncle Ben- Hide quoted text - > > - Show quoted text - I have been led through all this a few months ago, line at a time of the relevant section of the 1905 paper, by Androcles. Thank you Androcles. But my memory of the details have faded. OK, so Androcles is finding that Einstein's beta is 2 for v = 0.866c. In other words, the length of a rod measured in frame k (using xi and tau) is twice as big as it would be if measured in frame K (using x and t). That's fine isn't it? The rod is stationary withinin frame k so its length is easily measured as L within frame k. (Einstein's paper uses x' instead of L.) So xi=L gives the rod length in frame k. Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie we see the moving rod as shorter than it is measured in its rest frame.
From: Uncle Ben on 31 Jul 2010 09:15 On Jul 31, 8:36 am, ben6993 <ben6...(a)hotmail.com> wrote: > On Jul 31, 3:49 am, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > On Jul 30, 9:39 pm, blackhead <larryhar...(a)softhome.net> wrote: > > > > On 31 July, 01:46, Uncle Ben <b...(a)greenba.com> wrote: > > > > > On Jul 30, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > On Jul 30, 3:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > An apology to Androcles > > > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > > > sci.physics.relativity, was an error of confusing frames of > > > > > > reference. But I was wrong. > > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > > where x' is the length of a moving rod with respect to a stationary > > > > > > frame of reference K and xi is the length of the moving rod with > > > > > > respect to a frame k comoving with it. My difference with Androcles > > > > > > was that I claimed that xi is the proper length L of the rod and the > > > > > > shorter x' is a contracted length L/gamma. > > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > > > insists that x' is L and xi is an expanded length Lgamma. The proper > > > > > > length of the rod in k increases because of the existence of another > > > > > > frame of reference K moving with respect to it. (This other frame K is > > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > > considered moving the other way with respect to the rest frame k of > > > > > > the rod.) > > > > > > > This startling fresh idea would never have occurred to me without > > > > > > Androcles's guidance. > > > > > > > It seems strange that a nearby frame of reference K, by its relative > > > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > > > while the rod maintains a constant length with respect to K itself. > > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > > > on my cigar that had length L when I bought it. It seems strange that > > > > > > to you the cigar has length L, but because I am flying within your > > > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > > > idea that you are down there. > > > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > > > Uncle Ben > > > > > > In this rare instance of someone abandoning their constant delusional > > > > > denial state of existence, any chance you can take it a step further > > > > > and answer the following? > > > > > > Will the ripple eventually reach the Earth? If not then why not? > > > > > > 'Hubble Finds Ghostly Ring of Dark Matter'http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_featur... > > > > > > "Astronomers using NASAs Hubble Space Telescope got a first-hand view > > > > > of how dark matter behaves during a titanic collision between two > > > > > galaxy clusters. The wreck created a ripple of dark matter, which is > > > > > somewhat similar to a ripple formed in a pond when a rock hits the > > > > > water." > > > > > > The ripple will eventually reach the Earth and this is evidence dark > > > > > matter exists from the galaxy cluster to the Earth. This is evidence > > > > > dark matter is the medium of space in which light waves propagate.. > > > > > > Pressure exerted towards matter by dark matter displaced by the matter > > > > > is gravity.- Hide quoted text - > > > > > > - Show quoted text - > > > > > I have no idea, and this thread is abought the Einstein Expansion.- Hide quoted text - > > > > > - Show quoted text - > > > > Androcles rechristened the space LT as "Einstein's expansion" formula: > > > > xi = x'/sqrt(1 - v^2/c^2) with x' = x-vt > > > 1905 paper. > > > Used correctly, it transforms x coordinates of the same event between > > > different frames, not lengths directly. Androcles plugs in lengths for > > > xi, x' without considering what's involved in measuring a length. For > > > a start, it involves measuring space coordinates at the *same* time > > > and subtracting them from one another to get a length, if it's moving > > > in that frame. If the end points remain at the same locations for all > > > time, then simultaneity doesn't matter.- Hide quoted text - > > > > - Show quoted text - > > > Some ng history, Blackhead: > > > This subject has been discussed often, and in some discussions > > Androcles ha progressed all the way to a length comparison, following > > Einstein's 1905 paper. I now believe he has got it all right except > > for the final step, which is assigning values to x' and xi. He agrees > > in the meaning of the variables x' and xi, including correctly that > > x' < xi. Where he goes off the track is to insist that x'=L, and > > therefore xi= Lgamma. The correct path is to assign xi=L and conclude > > that x' = L/gamma. > > > The absurdity of this error is the point of this thread. > > > Uncle Ben- Hide quoted text - > > > - Show quoted text - > > I have been led through all this a few months ago, line at a time of > the relevant section of the 1905 paper, by Androcles. Thank you > Androcles. But my memory of the details have faded. > > OK, so Androcles is finding that Einstein's beta is 2 for v = 0.866c. > In other words, the length of a rod measured in frame k (using xi and > tau) is twice as big as it would be if measured in frame K (using x > and t). That's fine isn't it? > The rod is stationary withinin frame k so its length is easily > measured as L within frame k. (Einstein's paper uses x' instead of L.) > So xi=L gives the rod length in frame k. > Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie > we see the moving rod as shorter than it is measured in its rest frame.- Hide quoted text - > > - Show quoted text - Yes, namesake, the length in k is twice the length in K. The question is, are they 2L and L, or L and L/2. You (and everyone except Androcles) correctly argue for the latter. The former is absurd, since there are many conceivable K's existing simultaneously, each for a different v. For each, there is a different length xi w.r.t. k, which requires that xi have many values simultaneously. In the latter case, which you argue persuasively, xi is fixed at L, and for conceivable K there is its own contracted x'= L/gamma. Uncle Ben
From: ben6993 on 31 Jul 2010 09:35 On Jul 31, 2:15 pm, Uncle Ben <b...(a)greenba.com> wrote: > On Jul 31, 8:36 am, ben6993 <ben6...(a)hotmail.com> wrote: > > > > > > > On Jul 31, 3:49 am, Uncle Ben <b...(a)greenba.com> wrote: > > > > On Jul 30, 9:39 pm, blackhead <larryhar...(a)softhome.net> wrote: > > > > > On 31 July, 01:46, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > On Jul 30, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > On Jul 30, 3:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > > An apology to Androcles > > > > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles in > > > > > > > sci.physics.relativity, was an error of confusing frames of > > > > > > > reference. But I was wrong. > > > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > > > where x' is the length of a moving rod with respect to a stationary > > > > > > > frame of reference K and xi is the length of the moving rod with > > > > > > > respect to a frame k comoving with it. My difference with Androcles > > > > > > > was that I claimed that xi is the proper length L of the rod and the > > > > > > > shorter x' is a contracted length L/gamma. > > > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but he > > > > > > > insists that x' is L and xi is an expanded length Lgamma. The proper > > > > > > > length of the rod in k increases because of the existence of another > > > > > > > frame of reference K moving with respect to it. (This other frame K is > > > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > > > considered moving the other way with respect to the rest frame k of > > > > > > > the rod.) > > > > > > > > This startling fresh idea would never have occurred to me without > > > > > > > Androcles's guidance. > > > > > > > > It seems strange that a nearby frame of reference K, by its relative > > > > > > > motion, can expand a rod with respect to the rod's own proper frame k, > > > > > > > while the rod maintains a constant length with respect to K itself. > > > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) sucking > > > > > > > on my cigar that had length L when I bought it. It seems strange that > > > > > > > to you the cigar has length L, but because I am flying within your > > > > > > > frame of reference, my cigar is Lgamma long. In fact, because of your > > > > > > > frame of reference, the Concord is stretched by gamma for me but not > > > > > > > for you. I have no idea why my cigar is now longer, because I have no > > > > > > > idea that you are down there. > > > > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > > > > Uncle Ben > > > > > > > In this rare instance of someone abandoning their constant delusional > > > > > > denial state of existence, any chance you can take it a step further > > > > > > and answer the following? > > > > > > > Will the ripple eventually reach the Earth? If not then why not? > > > > > > > 'Hubble Finds Ghostly Ring of Dark Matter'http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_featur... > > > > > > > "Astronomers using NASAs Hubble Space Telescope got a first-hand view > > > > > > of how dark matter behaves during a titanic collision between two > > > > > > galaxy clusters. The wreck created a ripple of dark matter, which is > > > > > > somewhat similar to a ripple formed in a pond when a rock hits the > > > > > > water." > > > > > > > The ripple will eventually reach the Earth and this is evidence dark > > > > > > matter exists from the galaxy cluster to the Earth. This is evidence > > > > > > dark matter is the medium of space in which light waves propagate. > > > > > > > Pressure exerted towards matter by dark matter displaced by the matter > > > > > > is gravity.- Hide quoted text - > > > > > > > - Show quoted text - > > > > > > I have no idea, and this thread is abought the Einstein Expansion..- Hide quoted text - > > > > > > - Show quoted text - > > > > > Androcles rechristened the space LT as "Einstein's expansion" formula: > > > > > xi = x'/sqrt(1 - v^2/c^2) with x' = x-vt > > > > 1905 paper. > > > > Used correctly, it transforms x coordinates of the same event between > > > > different frames, not lengths directly. Androcles plugs in lengths for > > > > xi, x' without considering what's involved in measuring a length. For > > > > a start, it involves measuring space coordinates at the *same* time > > > > and subtracting them from one another to get a length, if it's moving > > > > in that frame. If the end points remain at the same locations for all > > > > time, then simultaneity doesn't matter.- Hide quoted text - > > > > > - Show quoted text - > > > > Some ng history, Blackhead: > > > > This subject has been discussed often, and in some discussions > > > Androcles ha progressed all the way to a length comparison, following > > > Einstein's 1905 paper. I now believe he has got it all right except > > > for the final step, which is assigning values to x' and xi. He agrees > > > in the meaning of the variables x' and xi, including correctly that > > > x' < xi. Where he goes off the track is to insist that x'=L, and > > > therefore xi= Lgamma. The correct path is to assign xi=L and conclude > > > that x' = L/gamma. > > > > The absurdity of this error is the point of this thread. > > > > Uncle Ben- Hide quoted text - > > > > - Show quoted text - > > > I have been led through all this a few months ago, line at a time of > > the relevant section of the 1905 paper, by Androcles. Thank you > > Androcles. But my memory of the details have faded. > > > OK, so Androcles is finding that Einstein's beta is 2 for v = 0.866c. > > In other words, the length of a rod measured in frame k (using xi and > > tau) is twice as big as it would be if measured in frame K (using x > > and t). That's fine isn't it? > > The rod is stationary withinin frame k so its length is easily > > measured as L within frame k. (Einstein's paper uses x' instead of L.) > > So xi=L gives the rod length in frame k. > > Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie > > we see the moving rod as shorter than it is measured in its rest frame.- Hide quoted text - > > > - Show quoted text - > > Yes, namesake, the length in k is twice the length in K. The question > is, are they 2L and L, or L and L/2. You (and everyone except > Androcles) correctly argue for the latter. > > The former is absurd, since there are many conceivable K's existing > simultaneously, each for a different v. For each, there is a different > length xi w.r.t. k, which requires that xi have many values > simultaneously. > > In the latter case, which you argue persuasively, xi is fixed at L, > and for conceivable K there is its own contracted x'= L/gamma. > > Uncle Ben- Hide quoted text - > > - Show quoted text - OK, I see, the question is whether it is L and 2L or L/2 and L? L cannot be measured with a ruler in frame K as the rod is moving in frame K. So it must be measured within frame k, by someone in frame k, with say a ruler. Noone in frame k is going to measure it and say that it is 2 times 3 feet long. They would instead say it is 6 feet long. L = 6 feet. In frame K the length of the rod is calculated as L/2 = 3 feet. I don't see where 2L arises as it does not occur in the calculation of x (from a given a value of xi) and it is not a ruler measurement of xi? It can only be 2L if the formula is used to calculate xi from a given value of x, and that cannot happen as noone is in a position to measure rod length x with a ruler in frame K (as th erod is moving) and then apply the formula to calculate xi. xi is measured with a ruler. x is calculated from the formula.
From: Androcles on 31 Jul 2010 09:34
"ben6993" <ben6993(a)hotmail.com> wrote in message news:04c03713-3840-4dd5-b9bd-0a32c3298392(a)w12g2000yqj.googlegroups.com... On Jul 31, 3:49 am, Uncle Ben <b...(a)greenba.com> wrote: > On Jul 30, 9:39 pm, blackhead <larryhar...(a)softhome.net> wrote: > > > > > > > On 31 July, 01:46, Uncle Ben <b...(a)greenba.com> wrote: > > > > On Jul 30, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Jul 30, 3:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > An apology to Androcles > > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles > > > > > in > > > > > sci.physics.relativity, was an error of confusing frames of > > > > > reference. But I was wrong. > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > where x' is the length of a moving rod with respect to a > > > > > stationary > > > > > frame of reference K and xi is the length of the moving rod with > > > > > respect to a frame k comoving with it. My difference with > > > > > Androcles > > > > > was that I claimed that xi is the proper length L of the rod and > > > > > the > > > > > shorter x' is a contracted length L/gamma. > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but > > > > > he > > > > > insists that x' is L and xi is an expanded length Lgamma. The > > > > > proper > > > > > length of the rod in k increases because of the existence of > > > > > another > > > > > frame of reference K moving with respect to it. (This other frame > > > > > K is > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > considered moving the other way with respect to the rest frame k > > > > > of > > > > > the rod.) > > > > > > This startling fresh idea would never have occurred to me without > > > > > Androcles's guidance. > > > > > > It seems strange that a nearby frame of reference K, by its > > > > > relative > > > > > motion, can expand a rod with respect to the rod's own proper > > > > > frame k, > > > > > while the rod maintains a constant length with respect to K > > > > > itself. > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) > > > > > sucking > > > > > on my cigar that had length L when I bought it. It seems strange > > > > > that > > > > > to you the cigar has length L, but because I am flying within your > > > > > frame of reference, my cigar is Lgamma long. In fact, because of > > > > > your > > > > > frame of reference, the Concord is stretched by gamma for me but > > > > > not > > > > > for you. I have no idea why my cigar is now longer, because I have > > > > > no > > > > > idea that you are down there. > > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to us. > > > > > > Uncle Ben > > > > > In this rare instance of someone abandoning their constant > > > > delusional > > > > denial state of existence, any chance you can take it a step further > > > > and answer the following? > > > > > Will the ripple eventually reach the Earth? If not then why not? > > > > > 'Hubble Finds Ghostly Ring of Dark > > > > Matter'http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_featur... > > > > > "Astronomers using NASA�s Hubble Space Telescope got a first-hand > > > > view > > > > of how dark matter behaves during a titanic collision between two > > > > galaxy clusters. The wreck created a ripple of dark matter, which is > > > > somewhat similar to a ripple formed in a pond when a rock hits the > > > > water." > > > > > The ripple will eventually reach the Earth and this is evidence dark > > > > matter exists from the galaxy cluster to the Earth. This is evidence > > > > dark matter is the medium of space in which light waves propagate. > > > > > Pressure exerted towards matter by dark matter displaced by the > > > > matter > > > > is gravity.- Hide quoted text - > > > > > - Show quoted text - > > > > I have no idea, and this thread is abought the Einstein Expansion.- > > > Hide quoted text - > > > > - Show quoted text - > > > Androcles rechristened the space LT as "Einstein's expansion" formula: > > > xi = x'/sqrt(1 - v^2/c^2) with x' = x-vt > > 1905 paper. > > Used correctly, it transforms x coordinates of the same event between > > different frames, not lengths directly. Androcles plugs in lengths for > > xi, x' without considering what's involved in measuring a length. For > > a start, it involves measuring space coordinates at the *same* time > > and subtracting them from one another to get a length, if it's moving > > in that frame. If the end points remain at the same locations for all > > time, then simultaneity doesn't matter.- Hide quoted text - > > > - Show quoted text - > > Some ng history, Blackhead: > > This subject has been discussed often, and in some discussions > Androcles ha progressed all the way to a length comparison, following > Einstein's 1905 paper. I now believe he has got it all right except > for the final step, which is assigning values to x' and xi. He agrees > in the meaning of the variables x' and xi, including correctly that > x' < xi. Where he goes off the track is to insist that x'=L, and > therefore xi= Lgamma. The correct path is to assign xi=L and conclude > that x' = L/gamma. > > The absurdity of this error is the point of this thread. > > Uncle Ben- Hide quoted text - > > - Show quoted text - I have been led through all this a few months ago, line at a time of the relevant section of the 1905 paper, by Androcles. Thank you Androcles. But my memory of the details have faded. OK, so Androcles is finding that Einstein's beta is 2 for v = 0.866c. In other words, the length of a rod measured in frame k (using xi and tau) is twice as big as it would be if measured in frame K (using x and t). That's fine isn't it? The rod is stationary withinin frame k so its length is easily measured as L within frame k. (Einstein's paper uses x' instead of L.) So xi=L gives the rod length in frame k. Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie we see the moving rod as shorter than it is measured in its rest frame. ================================================= You are wanking your brain to agree with your prejudice. "It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it ``the time of the stationary system.'' "Let there be given a stationary rigid rod; and let its length be L as measured by a measuring-rod which is also stationary." So tau = t/2 , moving clocks run slow. xi = 2L, moving rods grow longer. xi does not equal L, xi = 2L. Ie we see the moving rod as LONGER than it is measured in THE rest frame. End of fuckin' story, no further mental masturbation needed. |